A day before uninsured Americans could start signing up for coverage under the Affordable Care Act, the law at the heart of the divisive budget debate, President Obama seemed self-assured as the hours ticked away toward a government shutdown.

While the White House waited for the Republican-controlled House and the Democratic-led Senate to go through the final motions to make their budget impasse official, Obama said: “The Affordable Care Act is moving forward. That funding is already in place. You can’t shut it down.”

Millions of uninsured Americans have their first chance to sign up for what the administration says will be high-quality, affordable health coverage, achieving what presidents of both parties sought unsuccessfully for more than 60 years.

Even as the government-shutdown debate raged, the White House juggled the last-minute practical and communications work of putting a core piece of the law into effect Tuesday.

That was the long-anticipated start of open enrollment for the health-insurance marketplaces — known as exchanges — that are intended to eventually make competitively priced coverage available to the estimated 15 percent of uninsured Americans.

Republicans have voted more than 40 times to dismantle Obamacare. With just days before enrollment begins, a group led their most audacious effort to destroy the law by removing money for it.

House Speaker John Boehner on Monday urged the House to pass its latest plan, which delays by a year the mandate that uninsured individuals buy health coverage and prevents the government from making contributions to the health care of lawmakers, their staffs and political appointees.

But even with the shutdown, Americans on Tuesday will be able to go online in every state to compare and buy health plans sold in their market.

Coverage kicks off Jan. 1. But consumers have six months, through March 31, to sign up for coverage in the first year.

Opinion polls show a slight majority of Americans disapprove of the law.

But if Americans come to think they are getting a good deal on insurance, critics will have little ammunition to dismantle the Affordable Care Act.

There are still plenty of obstacles for the law’s supporters.

Federal officials initially missed a number of deadlines to hire and train the counselors who will help Americans enroll.

On Thursday, they announced the Spanish language and small-business marketplaces will not be ready this week.

Early implementation efforts were so clunky that Sen. Max Baucus, D-Montana, who wrote much of the health-care law, warned it could be headed for a “train wreck.”

But Health and Human Services Secretary Kathleen Sebelius has promised: “We are on target and ready to flip the switch on Oct. 1.”

The Treasury Department has also delayed by a year the requirement that businesses with 50 or more full-time employees provide coverage for their workers or face a fine — a move that the administration said was proof of its flexibility but one that opponents contended was an early warning of disaster.

About 6.4 million poor people will be left behind because they live in states that either have chosen not to broaden eligibility for their Medicaid programs or have not made a decision, according to a recent analysis by the Henry J. Kaiser Family Foundation.

Implementing a big new law “is not sexy. It’s not exciting. But it’s critically important, and it’s incredibly hard,” said Gautam Mukunda, author of the book “Indispensable: When Leaders Really Matter.”

In the case of the Affordable Care Act, implementation is made all the more difficult by how many moving parts are outside the president’s reach.

“I think you should expect many glitches,” said Jonathan Cohen, author of a book called “Sick,” and a journalist who believes the law is flawed but a vast improvement over the current health-care system.

Cohen predicted there will be problems with the computer system initially and perhaps a wait for services if many people enroll right away.

The federal government had to build a data hub, designed to link up with various federal databases, to check vital statistics about people applying for coverage to ensure they are eligible and determine what kind of financial help they may get. Will it be slow? Could it crash?

In surveys, uninsured Americans used words like “stressed and overwhelmed” to describe their feelings about signing up for health coverage, said Rachel Klein, who formerly worked with Enroll America, an organization focused on finding people who could benefit from the law.

“It’s not the kind of thing that inspires action. It’s the kind of the thing that makes you want to hide under the bed,” she said.

Along the way, Obama has tried to lower expectations.

“This is a big country, and the health-care industry is massive, and there are tons of providers and so as we implement, there are going to be glitches and there’s going to be certain states that for political reasons are resisting implementation and we’re just steadily working through all that stuff,” he said.

The most basic worry among the law’s proponents: They built it, but will Americans come?

It would be unfair to judge the law’s success by enrollment figures the first day or even the first few months, supporters argue.

Yet those who want the law to succeed and those who hope to undermine it will watch Tuesday carefully.

“Oct. 1 is certainly a symbolic day,” said Brad Woodhouse, president of Americans United for Change.

“It’s the beginning of the process. I don’t think anyone should look at Oct. 1 like they would look at Election Day in a presidential election year.”

What Woodhouse means is that at Tuesday’s end, the verdict will still be out on the health-care law.

Compiled from The New York Times, The Washington Post and The Palm Beach Post